Scale dependence of fractal dimension in deterministic and stochastic Lorenz-63 systems

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of deterministic chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively by studying the properties of the underlying attractor, the compact object asymptotically hosting the trajectories of the system with their invariant density in the phase space. This multi-scale nature of natural systems makes it practically impossible to get a clear picture of the attracting set. Indeed, it spans over a wide range of spatial scales and may even change in time due to non-stationary forcing. Here, we combine an adaptive decomposition method with extreme value theory to study the properties of the instantaneous scale-dependent dimension, which has been recently introduced to characterize such temporal and spatial scale-dependent attractors in turbulence and astrophysics. To provide a quantitative analysis of the properties of this metric, we test it on the well-known low-dimensional deterministic Lorenz-63 system perturbed with additive or multiplicative noise. We demonstrate that the properties of the invariant set depend on the scale we are focusing on and that the scale-dependent dimensions can discriminate between additive and multiplicative noise despite the fact that the two cases have exactly the same stationary invariant measure at large scales. The proposed formalism can be generally helpful to investigate the role of multi-scale fluctuations within complex systems, allowing us to deal with the problem of characterizing the role of stochastic fluctuations across a wide range of physical systems.

BepiColombo mission confirms stagnation region of Venus and reveals its large extent

The second Venus flyby of the BepiColombo mission offer a unique opportunity to make a complete tour of one of the few gas-dynamics dominated interaction regions between the supersonic solar wind and a Solar System object. The spacecraft pass through the full Venusian magnetosheath following the plasma streamlines, and cross the subsolar stagnation region during very stable solar wind conditions as observed upstream by the neighboring Solar Orbiter mission. These rare multipoint synergistic observations and stable conditions experimentally confirm what was previously predicted for the barely-explored stagnation region close to solar minimum. Here, we show that this region has a large extend, up to an altitude of 1900 km, and the estimated low energy transfer near the subsolar point confirm that the atmosphere of Venus, despite being non-magnetized and less conductive due to lower ultraviolet flux at solar minimum, is capable of withstanding the solar wind under low dynamic pressure.

Inner southern magnetosphere observation of Mercury via SERENA ion sensors in BepiColombo mission

Mercury's southern inner magnetosphere is an unexplored region as it was not observed by earlier space missions. In October 2021, BepiColombo mission has passed through this region during its first Mercury flyby. Here, we describe the observations of SERENA ion sensors nearby and inside Mercury's magnetosphere. An intermittent high-energy signal, possibly due to an interplanetary magnetic flux rope, has been observed downstream Mercury, together with low energy solar wind. Low energy ions, possibly due to satellite outgassing, were detected outside the magnetosphere. The dayside magnetopause and bow-shock crossing were much closer to the planet than expected, signature of a highly eroded magnetosphere. Different ion populations have been observed inside the magnetosphere, like low latitude boundary layer at magnetopause inbound and partial ring current at dawn close to the planet. These observations are important for understanding the weak magnetosphere behavior so close to the Sun, revealing details never reached before.

A discrete dynamical system: The poor man's magnetohydrodynamic (PMMHD) equations

A discrete dynamical system is derived, via a Fourier-Galerkin procedure, from three-dimensional equations describing incompressible plasmas in the magnetohydrodynamic (MHD) framework. The obtained six-dimensional (6D) map, consisting of logistic and nonlinear terms, can provide useful insights into incompressible plasmas dynamics when bifurcation parameters, controlling dissipative and coupling terms, are changed. The map preserves the total energy in the ideal MHD approximation (i.e., by neglecting dissipative terms), manifests a sensitive dependence to the initial conditions as well as at least one Lyapunov exponent is positive (as for chaotic systems), and is characterized by a dissipative nature of its phase space. Moreover, all fixed points of the usual MHD equations are recovered, including the fluid fixed point, the Alfvénic point, and the Taylor force-free solution. Finally, also some interesting properties, as the existence of a kinematic dynamo action, are evidenced, suggesting that discrete dynamical systems deserve consideration for the description of incompressible plasmas.

Spatial interactions in a modified Daisyworld model: Heat diffusivity and greenhouse effects

In this work we investigate a modified version of the Daisyworld model, originally introduced by Lovelock and Watson to describe in a simple way the interactions between an Earth-like planet, its biosphere, and the incoming solar radiation. Here a spatial dependency on latitude is included, and both a variable heat diffusivity along latitudes and a simple greenhouse effect description are introduced in the model. We show that the spatial interactions between the variables of the system can locally stabilize the coexistence of the two vegetation types. The feedback on albedo is able to generate equilibrium solutions which can efficiently self-regulate the planet climate, even for values of the solar luminosity relatively far from the current Earth conditions.

Untersuchung der Reliabilität der deutschen Version des Barthel-Index sowie Entwicklung einer postalischen und telefonischen Fassung für den Einsatz bei Schlaganfall-Patienten

BACKGROUND AND PURPOSES

Aim of the study was to translate the original version of the Barthel-Index (BI) into German and to investigate the reliability of the German version. In addition, a German version of the BI for postal and telephone use was developed.

METHODS

Data were collected in four neurological hospitals in Germany. The translation of the BI followed the protocol of the Medical Outcomes Trust. The interrater reliability of the German version of the BI was investigated in 72 patients after acute stroke. The reliability of the postal and telephone version of the BI was compared with face-to-face interview in 147 patients three months after stroke. Reliability was assessed using simple weighted kappa-statistics.

RESULTS

The interrater reliability of the German version of the BI was excellent (mean kappa 0.93). The mean kappa coefficient was 0.79 for the postal version of the BI and 0.80 for the telephone version. Thus, the agreement between the postal and the telephone administration of the BI compared to the face-to-face interview was substantial to excellent.

CONCLUSIONS

Our study published the first German version of the BI which was investigated for interrater reliability in a standardized way. The development of a postal and a telephone version allows the widespread use of the German BI for the follow up of stroke patients in different access paths.

[4 cases of Horton's temporal arteritis. Hypothesis on the possible correlations with rheumatic polymyalgia]

Giant cell arteritis (GCA) or temporal arteritis is an entity of unknown aetiology and uncertain autonomy for the close relationship with polymyalgia rheumatica (PMR). This work describes four patients with GCA alone. All patients had clinical and laboratoristic evidence of the disease and were treated with steroids. The distribution of HLA antigens showed an increased occurrence of DR4 and B8 antigens. Unfortunately, the small number of patients and the short period of observation don't allow to prove the exact nature of the link between GCA and PMR.